Question

Can you take 1 damage from a super-effective damage?

Comments

Shedinja can :P

Answer 1

You can, and in fact you can even take 0 damage from a super effective move. See https://replay.pokemonshowdown.com/gen7doublesubers-848387078 for a bunch of carefully orchestrated examples.

Answer 2

Yes.

-6 Lvl 1 0- Atk Frillish Poison Sting vs. 252 HP / 252+ Def Kebia Berry Dynamax Leafeon: 1-2 (0.1 - 0.2%) -- possibly the worst move ever
Possible damage amounts: (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2)

I chose Frillish because it has exceptionally low Attack, and Leafeon because it has rather high Defense. -6 Level 1 Frillish with an Attack-reducing Nature against max EV and Defense-boosting Nature Dynamax Leafeon with a Kebia Berry (which reduces damage from Poison moves) is pretty much a guarantee that your Frillish isn't going to be doing a thing.

Comments

Also Shedinja.

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I completely forgot about Shedinja's existence while writing this :P